The invention relates to the field of control systems, in general, and more particularly, to the field of anti-windup systems for control systems having a nonlinearity in the system between the command input and the system output.
It is commonly found in control systems that a phenomenon known as integrator windup may occur if compensators having integrators are used with actuators which have limited dynamic range. A typical control system will have a command input which receives a command signal which is summed with a feedback signal to create an error signal. This error signal is applied to the input of a compensator which usually has an integrator therein to smooth out instantaneous changes in the error signal. The output of the compensator is typically applied to the input of an actuator conversion device which converts the integrated error signal to another signal suitable for controlling the device being controlled. Integrator windup typically occurs when a large command input suddenly occurs which causes the actuator to saturate. Saturation of the actuator occurs when the output of the actuator can no longer increase or decrease with increasing or decreasing actuator input. Such saturation can result from either static or dynamic nonlinearities.
An example of a static nonlinearity is a variable power supply which can supply a maximum of 40 amps and a minimum of 10 amps in response to a command input. If a command input of 4 volts corresponds to an output of 40 amperes and a command input of 1 volt corresponds to an output of 10 amperes, then saturation occurs when the command input reaches and exceeds 4 volts. Even though the command input may be increasing to, for example, 5 or 6 volts, the output of the power supply cannot increase and remains constant at 40 amps.
An example of a dynamic nonlinearity is a slew rate limit. For example, if the output of an operational amplifier can only change 10 milliamperes per second for an input voltage which is changing 1 millivolt per second, saturation by slew rate limiting occurs when the input is changing at a rate faster than 1 millivolt per second. In other words, even though the input may be changing at 2 millivolts per second, the output is only changing at the maximum slew rate of 10 milliamperes per second.
The problem of integrator windup therefore is endemic to many different types of control systems using many different types of actuators involving both static and dynamic nonlinearities.
When saturation occurs, the output of the plant may not have reached the desired level commanded by the command input. As a result, a non-zero error signal will exist which will cause the output of the compensator to continue to change. However, even though the compensator output is still changing, no further change in the actuator output will result because the actuator has saturated. Since the integrator in the compensator keeps integrating the non-zero error signal, the output of the compensator continues to grow. However, the input to the plant is still at its maximum value, and therefore the error signal remains large. Thus, the increase in the output of the compensator is not helping anything, since the input to the plant is not changing.
The integrator output may be quite large if saturation lasts a long time. It takes considerable control effort to bring the output of the integrator back down to a reasonable value for subsequent operations. The result is that the plant output overshoots the desired level and remains at too high a level during the time it takes for the system to settle out and come out of saturation.
This overshoot is undesirable for most, if not all applications. Accordingly, a need has arisen for a control system which can adjust the error signal in such a way that overshoot and extended saturation does not occur.